Consider the 57 N weight held by two cables
shown below. The left-hand cable is horizon-
tal.
57 N
52�
a) What is the tension in the cable slanted
at an angle of 52�?
Answer in units of N
T2=mg/sin52 =57/0.788=72.3 N
T1 = T2cos52=72.3•0.616= 44.5 N
Well, well, well. Looks like we've got a tension-filled situation here. So, you've got a 57 N weight being held by two cables, with one cable slanted at an angle of 52 degrees. And you want to know the tension in that slanted cable, huh?
Alright, let's get to the bottom of this. Now, here's the deal. The horizontal cable doesn't really contribute to the tension in the slanted cable. It's just...there, being horizontal and stuff.
So, all the tension is being handled by our slanted cable hero. We can break down forces into their vertical and horizontal components. In this case, the vertical component of tension pulls upwards to counteract the weight, while the horizontal component just kinda chills out and doesn't do much.
Now, we can use some trigonometry to figure out the vertical component of tension. Since we know the angle (52 degrees) and the weight (57 N), we can use some sine magic to solve the equation.
So, Tension (vertical) = Weight / sin(angle) = 57 N / sin(52) = approximately 73.15 N.
Boom! There you have it. The tension in the slanted cable is approximately 73.15 N units of tension. Keep on hanging in there!
To find the tension in the cable slanted at an angle of 52 degrees, we can break down the weight into its vertical and horizontal components.
The vertical component of the weight can be found using the equation:
Weight_vertical = Weight * sin(angle)
Weight_vertical = 57 N * sin(52 degrees)
Weight_vertical ≈ 44.02 N
The tension in the slanted cable is equal to the vertical component of the weight. Therefore, the tension in the cable slanted at an angle of 52 degrees is approximately 44.02 N.
To find the tension in the cable slanted at an angle of 52 degrees, we can use trigonometry. The weight of 57 N is being supported by two cables, one horizontal and one slanted.
Let's denote the tension in the horizontal cable as T_horizontal and the tension in the slanted cable as T_slanted.
Since the left-hand cable is horizontal, its tension, T_horizontal, is equal to the weight of 57 N.
Now, let's focus on the cable slanted at an angle of 52 degrees. We can break down the weight into vertical and horizontal components using trigonometric functions.
The vertical component of the weight is given by:
Vertical component = Weight * sin(angle)
Vertical component = 57 N * sin(52 degrees)
The vertical component of the weight is equal to the tension in the slanted cable, T_slanted. So we have:
T_slanted = 57 N * sin(52 degrees)
Now, we can calculate this value:
T_slanted = 57 N * sin(52 degrees)
T_slanted ≈ 57 N * 0.788
T_slanted ≈ 44.9 N
Therefore, the tension in the cable slanted at an angle of 52 degrees is approximately 44.9 N.